I bought one in 7mm-08 last year. Worst shooter I have ever bought. Horribly inconsistent. I know a few other local guys that have the same problems.
After boxes of ammo, pounds of powder, and boxes of bullets it went to get a new barrel.
Rifle $525, new barrel $812. These are Canadian prices.
Bought a weatherby vanguard (cost was $400) for my gf. Out of the box cloverleaf 5 round groups. Hers is a 243.
Now these guns sell for $950-1300 and the new tacticool one is over $2500. Not a chance I would buy another
Im not trying to argue with you or change your mind about Tikka rilfes, and I can not speek to the T3 Lite's replacement the T3x, but six years ago my friend wanted my advice on his very first high powered center fire rifle purchase as he finally was going to start hunting out west. He also at that time didn't own a computer and had little access to the internet to visit websites such as this for advice.
I spent literally dozens of hours on every website I could find gathering data on sub $1000 rifles from Winchester, Remington, Marlin, T/C, Browning, to name a few and consequently I read HUNDREDS of rifle reviews on every sub $1000 dollar rile I could find solid information on in production at that time, printed out a great many of them and created a evaluation chart of sorts for all rifles being considered and in the end I recommended he buy A Tikka T3 lite. The over whelming reason I recommended a Tikka T3 was I read exactly ZERO reports or reviews that were SIGNIFICANTLY negative. They all said BASICALLY the same thing: Superb accuracy, great trigger, excellent if not unbeatable value for the money.
Yes there were some minor complaints about Tikka T3 lites such as concerning the rings holding up for heavier recoiling calibers, to short a magazine, you have to remove the stock to adjust the trigger, barrel not having a target crown, but none of the rifles in it's price range had fewer complaints, and none of the complaints I found had any bearing on it's abilities to do what it was designed for.
I know every manufacturer of all things mechanical or otherwise produce failures, and I can believe your T3 was one of them, but for as you said at least 2 or more of your friends to have bought T3's that all were lemons I find nearly a statistical impossibility based on I have NEVER heard of such a thing happening with T3 lites.
And even though my T3 is by far nor just the most accurate rifle I have ever shot, it is also with factory as well as quite a few of the reloads I have fed it thus far, I have a complaint, well kind of a complaint about my T3 Lite.
I found out that very light rifles like the T3 are considerably harder to shoot from the bench than heavier rifles and are much more affected by inconsistent bench form then any rifle (and I own quite a few) that I have ever shot. Use the same exact bench form and my T3 gives me absolute bug holes. I have an honest 1/2 dozen 3-shot 100 yard groups under .5", and yes I know most at this website feel 3 shot 100 yard groups are all but meaningless, but for me they are not.
BUT, let me be the least little bit sloppy or inconsistent in my bench form and my groups instantly open up to at or above 2". I admit this is a more serious issue with my Tikka VS my other rifles.
I'm sorry to here of your problems and I would send the rifle back to Tikka if you still own it, but your experience is IMHO in the 5 percentile or less or Tikka T3 lite owners results.